A Comment on Curvature Effects In CFTs And The Cardy-Verlinde Formula

TL;DR

This paper investigates curvature effects on the Cardy-Verlinde formula in N=4 Super Yang-Mills theory and its AdS dual, revealing corrections that modify the formula and show its exactness on the gravity side.

Contribution

It introduces a modified Cardy-Verlinde formula accounting for curvature effects in SYM theory and demonstrates its exactness in the AdS gravity dual.

Findings

Curvature effects cause non-trivial corrections to thermodynamic quantities.

A modified Cardy-Verlinde formula is derived for SYM theory.

The corrections imply the formula is exact in the gravity dual.

Abstract

We examine the Cardy-Verlinde formula for finite temperature N=4 Super Yang-Mills theory on $R\times S^3$, and its AdS dual. We find that curvature effects introduce non-trivial corrections to thermodynamic quantities computed on both sides. We find a modified version of the Cardy-Verlinde formula for the SYM theory, incorporating these. On the gravity side, these corrections imply that the Cardy-Verlinde formula is exact.